Breeding of crops with high levels of minerals,vitamins,and proteins is called:

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ L \ mol^{-1}$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

If the transverse and conjugate axes of a hyperbola are equal,then its eccentricity is

The wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \mathring{A}}$ and ${\lambda _2 = 5000 \ \mathring{A}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

In an experiment with $15$ observations on $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

Two blocks are connected by a spring. The combination is suspended,at rest,from a string attached to the ceiling,as shown in the figure. The string breaks suddenly. Immediately after the string breaks,what is the initial downward acceleration of the upper block of mass $2\,m$?